 Hello and welcome to the session. In this session we discussed the chronic question which says, from an external point Q, tangents Qt and Qt dash are drawn to a circle with center O. If p s is the tangent to the circle at a point A and Qt is equal to 10 centimeters, find the perimeter of triangle Qps. Before moving on to the solution let's recall one fact which says that the lengths of tangents drawn from an external point to a circle are equal. This is the key idea that we use in this question. Now let's proceed with the solution. Consider this figure. Let's see what all is given to us in the question. We are given that Qt and Qt dash are tangents to the circle. Then p s is also a tangent to the circle at point A and we are given that Qt is equal to 10 centimeters. We need to find the perimeter of triangle Qps. Now since we know that the lengths of the tangents drawn from an external point to a circle are equal, therefore we have Qt is equal to Qt dash since they are the tangents from the external point Q. Then also we have pt is equal to pa as they are the tangents from the point p. Also as is equal to st dash as they are also the tangents from the point s. Now the perimeter of the triangle Qps is equal to the sum of the three sides of this triangle that is Qp plus ps plus sq. Now from the figure we have that Qp is equal to Qt minus pt then ps is equal to pa plus as and sq is equal to Qt dash minus st dash. Now since we have pt is equal to pa therefore this would be further equal to Qt minus pa plus pa plus as plus. Now st dash is equal to as so here we can have Qt dash minus as so this is equal to Qt minus pa plus pa plus as plus Qt dash minus as now pa and minus pa cancels as and minus as cancels and this is equal to Qt plus Qt dash. So we have the perimeter of triangle Qps is equal to Qt plus Qt dash and this is equal to two times Qt since we know that Qt is equal to Qt dash. And we are given that Qt is equal to ten centimeters therefore we get the perimeter of triangle Qps is equal to two into ten centimeters that is equal to twenty centimeters is the perimeter of triangle Qps. So twenty centimeters is the required answer. This completes the session. Hope you have understood the solution of this question.